# Probability and Statistics. Random Sampling

Random sampling is defined as a sampling method whereby several subjects are selected for a study from a population. Each member of the population is merely chosen by chance and therefore each member of the population has an equal probability chance for being chosen for the study. On the other hand, non-random sampling may be defined as a technique whereby units are selected purposively, that is, members of the population are selected at fixed intervals on a list. Random sampling is preferred to non-random sampling because in the former the likelihood of bias is reduced.

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In addition, with non-random sampling, it becomes hard to conclude the entire population based on the information obtained from a sample (Pedhazur & Schmelkin, 1991). Simple random sampling can be defined as a sampling method where a set of subjects (sample) is chosen for a study from the entire population. Each member of the population has an equal chance of being selected at any level in the sampling process. In stratified sampling, the population is first divided into groups/strata, and then a sample for the study is obtained from each stratum of a population. Single-stage cluster sampling involves the partitioning of the entire population into suitable clusters then you randomly select the required number of clusters as sample items and further examine all the subjects in each of the randomly chosen clusters.

In the multi-stage technique, sampling is usually done in various stages (Stuart, 1962). For instance, each unit in the population is being divided into subunits and if these subunits within a selected unit give similar results, one may select and compute a sample of the subunits in any chosen unit without necessarily measuring all the units. Advantages of each of the following commonly used sampling techniques Simple random sampling is the simplest sampling technique when a small population is being considered. Stratified sampling focuses on important strata (subpopulations) and does not include irrelevant ones. This method always attains greater precision if the subpopulation chose posses similar characteristics being analyzed. It also gives room for various sampling methods to be used for different subpopulations.

The single-stage cluster sampling eliminates much of the difficulty involved in the estimation procedure which is required by two-stage cluster sampling. The multi-stage technique is more convenient and flexible compared to single-stage sampling. Since it can reduce to one-stage sampling, there is a chance of choosing a smaller value that is more efficient (Pedhazur & Schmelkin, 1991). Limitation of each of the following commonly used sampling techniques Simple random sampling is quite difficult to carry out if a large size of the population is being studied. The stratified method is irrelevant if heterogeneous subgroups are considered. In addition, this method is quite expensive to administer. It may be also difficult in some populations to divide into strata (Stuart, 1962). In a single-stage cluster, there is a high risk of sampling error involved. If the size of the population is not large enough, multi-stage sampling has a likelihood of giving inaccurate results.

## References

Pedhazur, E., & Schmelkin, L. (1991). Measurement design and analysis: An integrated approach. New York: Psychology Press.

Stuart, Alan (1962) Basic Ideas of Scientific Sampling, Hafner Publishing Company, New York.

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